Therefore in order to continue our study of local face distributions we need to better understand the class products \(C_d C_\lambda \) . A generating function for the number of elements in \(C_d C_\lambda \)  with a given number of cycles is given by Stanley [1]}. However for our applications we need to understand the whole cycle type, not just the number of cycles. In order to do this, we use a technique of Gamburd [2]} and Chmutov and Pittel [3]}. The main result of the next section is that, as long as \(\lambda \)  has not too many parts of size one, the distribution of \(C_d C_\lambda \)  is close to uniform (up to parity).
